Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1856,2,Mod(1217,1856)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1856, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1856.1217");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1856 = 2^{6} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1856.e (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.8202346151\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 928) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1217.2 | ||
Root | \(-0.618034i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1856.1217 |
Dual form | 1856.2.e.h.1217.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1856\mathbb{Z}\right)^\times\).
\(n\) | \(321\) | \(581\) | \(639\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | −0.957427 | − | 0.288675i | \(-0.906785\pi\) | ||
0.957427 | − | 0.288675i | \(-0.0932147\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | −0.223607 | − | 0.974679i | \(-0.571783\pi\) | ||||
−0.223607 | + | 0.974679i | \(0.571783\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.47214 | 1.69031 | 0.845154 | − | 0.534522i | \(-0.179509\pi\) | ||||
0.845154 | + | 0.534522i | \(0.179509\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.00000 | 0.666667 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.00000i | − | 0.904534i | −0.891883 | − | 0.452267i | \(-0.850615\pi\) | ||
0.891883 | − | 0.452267i | \(-0.149385\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | 0.138675 | − | 0.990338i | \(-0.455716\pi\) | ||||
0.138675 | + | 0.990338i | \(0.455716\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000i | 0.258199i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.47214i | − | 1.08465i | −0.840168 | − | 0.542326i | \(-0.817544\pi\) | ||
0.840168 | − | 0.542326i | \(-0.182456\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000i | 0.917663i | 0.888523 | + | 0.458831i | \(0.151732\pi\) | ||||
−0.888523 | + | 0.458831i | \(0.848268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 4.47214i | − | 0.975900i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.47214 | 0.932505 | 0.466252 | − | 0.884652i | \(-0.345604\pi\) | ||||
0.466252 | + | 0.884652i | \(0.345604\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.00000 | −0.800000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.00000i | − | 0.962250i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.00000 | + | 4.47214i | 0.557086 | + | 0.830455i | ||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.00000i | 0.898027i | 0.893525 | + | 0.449013i | \(0.148224\pi\) | ||||
−0.893525 | + | 0.449013i | \(0.851776\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.00000 | −0.522233 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.47214 | −0.755929 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 1.00000i | − | 0.160128i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4.47214i | − | 0.698430i | −0.937043 | − | 0.349215i | \(-0.886448\pi\) | ||
0.937043 | − | 0.349215i | \(-0.113552\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.00000i | 0.152499i | 0.997089 | + | 0.0762493i | \(0.0242945\pi\) | ||||
−0.997089 | + | 0.0762493i | \(0.975706\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.00000 | −0.298142 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.00000i | 0.437595i | 0.975770 | + | 0.218797i | \(0.0702134\pi\) | ||||
−0.975770 | + | 0.218797i | \(0.929787\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.0000 | 1.85714 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.47214 | −0.626224 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.00000 | 1.23625 | 0.618123 | − | 0.786082i | \(-0.287894\pi\) | ||||
0.618123 | + | 0.786082i | \(0.287894\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.00000i | 0.404520i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.00000 | 0.529813 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.47214 | −0.582223 | −0.291111 | − | 0.956689i | \(-0.594025\pi\) | ||||
−0.291111 | + | 0.956689i | \(0.594025\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 13.4164i | − | 1.71780i | −0.512148 | − | 0.858898i | \(-0.671150\pi\) | ||
0.512148 | − | 0.858898i | \(-0.328850\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.94427 | 1.12687 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.94427 | −1.09272 | −0.546358 | − | 0.837552i | \(-0.683986\pi\) | ||||
−0.546358 | + | 0.837552i | \(0.683986\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 4.47214i | − | 0.538382i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.94427 | −1.06149 | −0.530745 | − | 0.847532i | \(-0.678088\pi\) | ||||
−0.530745 | + | 0.847532i | \(0.678088\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.94427i | 1.04685i | 0.852072 | + | 0.523424i | \(0.175346\pi\) | ||||
−0.852072 | + | 0.523424i | \(0.824654\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.00000i | 0.461880i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 13.4164i | − | 1.52894i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.0000i | 1.68763i | 0.536633 | + | 0.843816i | \(0.319696\pi\) | ||||
−0.536633 | + | 0.843816i | \(0.680304\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.47214 | 0.490881 | 0.245440 | − | 0.969412i | \(-0.421067\pi\) | ||||
0.245440 | + | 0.969412i | \(0.421067\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.47214i | 0.485071i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.47214 | − | 3.00000i | 0.479463 | − | 0.321634i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 13.4164i | − | 1.42214i | −0.703123 | − | 0.711068i | \(-0.748212\pi\) | ||
0.703123 | − | 0.711068i | \(-0.251788\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.47214 | 0.468807 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.00000 | 0.518476 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 4.00000i | − | 0.410391i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 13.4164i | − | 1.36223i | −0.732177 | − | 0.681115i | \(-0.761495\pi\) | ||
0.732177 | − | 0.681115i | \(-0.238505\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 6.00000i | − | 0.603023i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 8.94427i | − | 0.889988i | −0.895533 | − | 0.444994i | \(-0.853206\pi\) | ||
0.895533 | − | 0.444994i | \(-0.146794\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.47214i | 0.436436i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.4164 | 1.29701 | 0.648507 | − | 0.761209i | \(-0.275394\pi\) | ||||
0.648507 | + | 0.761209i | \(0.275394\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.00000 | −0.0957826 | −0.0478913 | − | 0.998853i | \(-0.515250\pi\) | ||||
−0.0478913 | + | 0.998853i | \(0.515250\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 17.8885i | − | 1.68281i | −0.540403 | − | 0.841406i | \(-0.681728\pi\) | ||
0.540403 | − | 0.841406i | \(-0.318272\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.47214 | −0.417029 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.00000 | 0.184900 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 20.0000i | − | 1.83340i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.00000 | 0.181818 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.47214 | −0.403239 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.00000 | 0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 12.0000i | − | 1.06483i | −0.846484 | − | 0.532414i | \(-0.821285\pi\) | ||
0.846484 | − | 0.532414i | \(-0.178715\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.00000 | 0.0880451 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 17.8885i | 1.55113i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.00000i | 0.430331i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17.8885i | 1.52832i | 0.645026 | + | 0.764161i | \(0.276847\pi\) | ||||
−0.645026 | + | 0.764161i | \(0.723153\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.47214 | 0.379322 | 0.189661 | − | 0.981850i | \(-0.439261\pi\) | ||||
0.189661 | + | 0.981850i | \(0.439261\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.00000 | 0.252646 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 3.00000i | − | 0.250873i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.00000 | − | 4.47214i | −0.249136 | − | 0.371391i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 13.0000i | − | 1.07222i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.00000 | 0.0819232 | 0.0409616 | − | 0.999161i | \(-0.486958\pi\) | ||||
0.0409616 | + | 0.999161i | \(0.486958\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.4164 | −1.09181 | −0.545906 | − | 0.837846i | \(-0.683814\pi\) | ||||
−0.545906 | + | 0.837846i | \(0.683814\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 8.94427i | − | 0.723102i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 5.00000i | − | 0.401610i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.47214i | 0.356915i | 0.983948 | + | 0.178458i | \(0.0571108\pi\) | ||||
−0.983948 | + | 0.178458i | \(0.942889\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 9.00000i | − | 0.713746i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 20.0000 | 1.57622 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 1.00000i | − | 0.0783260i | −0.999233 | − | 0.0391630i | \(-0.987531\pi\) | ||
0.999233 | − | 0.0391630i | \(-0.0124692\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.00000 | 0.233550 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.94427 | −0.692129 | −0.346064 | − | 0.938211i | \(-0.612482\pi\) | ||||
−0.346064 | + | 0.938211i | \(0.612482\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.00000i | 0.611775i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.00000 | 0.456172 | 0.228086 | − | 0.973641i | \(-0.426753\pi\) | ||||
0.228086 | + | 0.973641i | \(0.426753\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −17.8885 | −1.35225 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.47214i | 0.336146i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.8885 | 1.33705 | 0.668526 | − | 0.743689i | \(-0.266925\pi\) | ||||
0.668526 | + | 0.743689i | \(0.266925\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −25.0000 | −1.85824 | −0.929118 | − | 0.369784i | \(-0.879432\pi\) | ||||
−0.929118 | + | 0.369784i | \(0.879432\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.4164 | −0.991769 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.4164 | −0.981105 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 22.3607i | − | 1.62650i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 8.00000i | − | 0.578860i | −0.957199 | − | 0.289430i | \(-0.906534\pi\) | ||
0.957199 | − | 0.289430i | \(-0.0934657\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 4.47214i | − | 0.321911i | −0.986962 | − | 0.160956i | \(-0.948542\pi\) | ||
0.986962 | − | 0.160956i | \(-0.0514576\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.00000i | 0.0716115i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.0000 | −1.56744 | −0.783718 | − | 0.621117i | \(-0.786679\pi\) | ||||
−0.783718 | + | 0.621117i | \(0.786679\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.47214 | 0.317021 | 0.158511 | − | 0.987357i | \(-0.449331\pi\) | ||||
0.158511 | + | 0.987357i | \(0.449331\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.94427i | 0.630880i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 13.4164 | + | 20.0000i | 0.941647 | + | 1.40372i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.47214i | 0.312348i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.94427 | 0.621670 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.0000 | 0.830057 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 27.0000i | 1.85876i | 0.369129 | + | 0.929378i | \(0.379656\pi\) | ||||
−0.369129 | + | 0.929378i | \(0.620344\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.94427i | 0.612851i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 1.00000i | − | 0.0681994i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 22.3607i | 1.51794i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.94427 | 0.604398 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 4.47214i | − | 0.300828i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.8885 | 1.19791 | 0.598953 | − | 0.800784i | \(-0.295584\pi\) | ||||
0.598953 | + | 0.800784i | \(0.295584\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.00000 | −0.533333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.8885 | 1.18730 | 0.593652 | − | 0.804722i | \(-0.297686\pi\) | ||||
0.593652 | + | 0.804722i | \(0.297686\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.3607i | 1.47764i | 0.673905 | + | 0.738818i | \(0.264616\pi\) | ||||
−0.673905 | + | 0.738818i | \(0.735384\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −13.4164 | −0.882735 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.00000 | −0.589610 | −0.294805 | − | 0.955557i | \(-0.595255\pi\) | ||||
−0.294805 | + | 0.955557i | \(0.595255\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 3.00000i | − | 0.195698i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.0000 | 0.974355 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.3607 | −1.44639 | −0.723196 | − | 0.690643i | \(-0.757328\pi\) | ||||
−0.723196 | + | 0.690643i | \(0.757328\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.0000 | −1.09507 | −0.547533 | − | 0.836784i | \(-0.684433\pi\) | ||||
−0.547533 | + | 0.836784i | \(0.684433\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 16.0000i | − | 1.02640i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.0000 | −0.830540 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.00000i | 0.254514i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 4.47214i | − | 0.283410i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.0000i | 1.45175i | 0.687828 | + | 0.725874i | \(0.258564\pi\) | ||||
−0.687828 | + | 0.725874i | \(0.741436\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 13.4164i | − | 0.843482i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.47214 | 0.280056 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.0000 | 1.06043 | 0.530215 | − | 0.847863i | \(-0.322111\pi\) | ||||
0.530215 | + | 0.847863i | \(0.322111\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.00000 | + | 8.94427i | 0.371391 | + | 0.553637i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 21.0000i | 1.29492i | 0.762101 | + | 0.647458i | \(0.224168\pi\) | ||||
−0.762101 | + | 0.647458i | \(0.775832\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.00000 | −0.552866 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −13.4164 | −0.821071 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.47214i | 0.272671i | 0.990663 | + | 0.136335i | \(0.0435325\pi\) | ||||
−0.990663 | + | 0.136335i | \(0.956467\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.0000i | 1.03268i | 0.856385 | + | 0.516338i | \(0.172705\pi\) | ||||
−0.856385 | + | 0.516338i | \(0.827295\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 4.47214i | − | 0.270666i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.0000i | 0.723627i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.0000 | 1.32185 | 0.660926 | − | 0.750451i | \(-0.270164\pi\) | ||||
0.660926 | + | 0.750451i | \(0.270164\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.0000i | 0.598684i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.00000 | −0.298275 | −0.149137 | − | 0.988816i | \(-0.547650\pi\) | ||||
−0.149137 | + | 0.988816i | \(0.547650\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.47214 | 0.265841 | 0.132920 | − | 0.991127i | \(-0.457565\pi\) | ||||
0.132920 | + | 0.991127i | \(0.457565\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.00000 | −0.236940 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 20.0000i | − | 1.18056i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.00000 | −0.176471 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.4164 | −0.786484 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.47214 | 0.260378 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −15.0000 | −0.870388 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.47214 | 0.258630 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.47214i | 0.257770i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.94427 | −0.513835 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.4164i | 0.768221i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 27.0000i | − | 1.54097i | −0.637457 | − | 0.770486i | \(-0.720014\pi\) | ||
0.637457 | − | 0.770486i | \(-0.279986\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.00000 | 0.0565233 | 0.0282617 | − | 0.999601i | \(-0.491003\pi\) | ||||
0.0282617 | + | 0.999601i | \(0.491003\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −8.94427 | −0.503953 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.47214i | 0.251180i | 0.992082 | + | 0.125590i | \(0.0400824\pi\) | ||||
−0.992082 | + | 0.125590i | \(0.959918\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.4164 | − | 9.00000i | 0.751175 | − | 0.503903i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 13.4164i | − | 0.748831i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 17.8885 | 0.995345 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.00000 | −0.221880 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.00000i | 0.0553001i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 13.4164i | 0.739671i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.0000i | 0.824475i | 0.911077 | + | 0.412237i | \(0.135253\pi\) | ||||
−0.911077 | + | 0.412237i | \(0.864747\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.94427 | 0.488678 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.3607i | 1.21806i | 0.793146 | + | 0.609032i | \(0.208442\pi\) | ||||
−0.793146 | + | 0.609032i | \(0.791558\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −17.8885 | −0.971572 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.0000 | 0.812296 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 26.8328 | 1.44884 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.47214i | 0.240772i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.8885 | −0.960307 | −0.480154 | − | 0.877184i | \(-0.659419\pi\) | ||||
−0.480154 | + | 0.877184i | \(0.659419\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.00000 | 0.481759 | 0.240879 | − | 0.970555i | \(-0.422564\pi\) | ||||
0.240879 | + | 0.970555i | \(0.422564\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 5.00000i | − | 0.266880i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.0000 | −0.745145 | −0.372572 | − | 0.928003i | \(-0.621524\pi\) | ||||
−0.372572 | + | 0.928003i | \(0.621524\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.94427 | 0.474713 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −20.0000 | −1.05851 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.0000i | 0.580558i | 0.956942 | + | 0.290279i | \(0.0937481\pi\) | ||||
−0.956942 | + | 0.290279i | \(0.906252\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 2.00000i | − | 0.104973i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 8.94427i | − | 0.468165i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.00000i | 0.417597i | 0.977959 | + | 0.208798i | \(0.0669552\pi\) | ||||
−0.977959 | + | 0.208798i | \(0.933045\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 8.94427i | − | 0.465620i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 40.2492 | 2.08964 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.0000 | −1.08734 | −0.543669 | − | 0.839299i | \(-0.682965\pi\) | ||||
−0.543669 | + | 0.839299i | \(0.682965\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 9.00000i | − | 0.464758i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.00000 | + | 4.47214i | 0.154508 | + | 0.230327i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 20.0000i | − | 1.02733i | −0.857991 | − | 0.513665i | \(-0.828287\pi\) | ||
0.857991 | − | 0.513665i | \(-0.171713\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.0000 | −0.614779 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.4164 | −0.685546 | −0.342773 | − | 0.939418i | \(-0.611366\pi\) | ||||
−0.342773 | + | 0.939418i | \(0.611366\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.4164i | 0.683763i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.00000i | 0.101666i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.94427i | 0.453493i | 0.973954 | + | 0.226746i | \(0.0728088\pi\) | ||||
−0.973954 | + | 0.226746i | \(0.927191\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 20.0000i | − | 1.01144i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 15.0000i | − | 0.754732i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.0000 | −0.652451 | −0.326226 | − | 0.945292i | \(-0.605777\pi\) | ||||
−0.326226 | + | 0.945292i | \(0.605777\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 17.8885 | 0.895547 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.0000 | 0.749064 | 0.374532 | − | 0.927214i | \(-0.377803\pi\) | ||||
0.374532 | + | 0.927214i | \(0.377803\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.00000i | 0.249068i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.8885i | 0.884532i | 0.896884 | + | 0.442266i | \(0.145825\pi\) | ||||
−0.896884 | + | 0.442266i | \(0.854175\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 17.8885 | 0.882377 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −20.0000 | −0.984136 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.47214 | −0.219529 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 4.47214i | − | 0.219001i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −35.7771 | −1.74783 | −0.873913 | − | 0.486083i | \(-0.838425\pi\) | ||||
−0.873913 | + | 0.486083i | \(0.838425\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.3050i | 1.52571i | 0.646570 | + | 0.762855i | \(0.276203\pi\) | ||||
−0.646570 | + | 0.762855i | \(0.723797\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.00000i | 0.291730i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17.8885i | 0.867722i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 60.0000i | − | 2.90360i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.00000 | −0.144841 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.47214 | −0.215415 | −0.107708 | − | 0.994183i | \(-0.534351\pi\) | ||||
−0.107708 | + | 0.994183i | \(0.534351\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 8.94427i | − | 0.429834i | −0.976632 | − | 0.214917i | \(-0.931052\pi\) | ||
0.976632 | − | 0.214917i | \(-0.0689481\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.47214 | + | 3.00000i | −0.214423 | + | 0.143839i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 17.8885i | 0.855725i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 40.2492 | 1.92099 | 0.960495 | − | 0.278296i | \(-0.0897697\pi\) | ||||
0.960495 | + | 0.278296i | \(0.0897697\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 26.0000 | 1.23810 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.00000i | 0.190046i | 0.995475 | + | 0.0950229i | \(0.0302924\pi\) | ||||
−0.995475 | + | 0.0950229i | \(0.969708\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.4164i | 0.635999i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 1.00000i | − | 0.0472984i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 17.8885i | − | 0.844213i | −0.906546 | − | 0.422106i | \(-0.861291\pi\) | ||
0.906546 | − | 0.422106i | \(-0.138709\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.4164 | −0.631754 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.4164i | 0.630358i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.47214 | −0.209657 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −38.0000 | −1.77757 | −0.888783 | − | 0.458329i | \(-0.848448\pi\) | ||||
−0.888783 | + | 0.458329i | \(0.848448\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −22.3607 | −1.04371 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 17.8885i | − | 0.833153i | −0.909101 | − | 0.416576i | \(-0.863230\pi\) | ||
0.909101 | − | 0.416576i | \(-0.136770\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.4164 | −0.623513 | −0.311757 | − | 0.950162i | \(-0.600917\pi\) | ||||
−0.311757 | + | 0.950162i | \(0.600917\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.00000 | −0.231869 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 37.0000i | 1.71216i | 0.516847 | + | 0.856078i | \(0.327106\pi\) | ||||
−0.516847 | + | 0.856078i | \(0.672894\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −40.0000 | −1.84703 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.47214 | 0.206065 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.00000 | 0.137940 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 16.0000i | − | 0.734130i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 18.0000 | 0.824163 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.00000i | 0.228456i | 0.993455 | + | 0.114228i | \(0.0364394\pi\) | ||||
−0.993455 | + | 0.114228i | \(0.963561\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 20.0000i | − | 0.910032i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.4164i | 0.609208i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 40.2492 | 1.82387 | 0.911933 | − | 0.410339i | \(-0.134590\pi\) | ||||
0.911933 | + | 0.410339i | \(0.134590\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.00000 | −0.0452216 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.0000i | 1.12823i | 0.825695 | + | 0.564117i | \(0.190783\pi\) | ||||
−0.825695 | + | 0.564117i | \(0.809217\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.0000 | − | 13.4164i | 0.900755 | − | 0.604245i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.00000i | 0.269680i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −40.0000 | −1.79425 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.4164 | −0.600601 | −0.300300 | − | 0.953845i | \(-0.597087\pi\) | ||||
−0.300300 | + | 0.953845i | \(0.597087\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.94427i | 0.399601i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.00000i | 0.401290i | 0.979664 | + | 0.200645i | \(0.0643038\pi\) | ||||
−0.979664 | + | 0.200645i | \(0.935696\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.94427i | 0.398015i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.0000i | 0.532939i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 25.0000 | 1.10811 | 0.554053 | − | 0.832482i | \(-0.313081\pi\) | ||||
0.554053 | + | 0.832482i | \(0.313081\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 40.0000i | 1.76950i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 20.0000 | 0.883022 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.00000 | 0.395820 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 6.00000i | − | 0.263371i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.0000 | −1.00765 | −0.503824 | − | 0.863806i | \(-0.668074\pi\) | ||||
−0.503824 | + | 0.863806i | \(0.668074\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.8328 | −1.17332 | −0.586659 | − | 0.809834i | \(-0.699557\pi\) | ||||
−0.586659 | + | 0.809834i | \(0.699557\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 17.8885i | 0.780720i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 22.3607 | 0.974047 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.00000 | −0.130435 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.94427 | −0.388148 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 4.47214i | − | 0.193710i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.4164 | −0.580042 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 17.8885i | − | 0.771948i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 39.0000i | − | 1.67985i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.7771i | 1.53818i | 0.639142 | + | 0.769089i | \(0.279290\pi\) | ||||
−0.639142 | + | 0.769089i | \(0.720710\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 25.0000i | 1.07285i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.00000 | 0.0428353 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.47214 | −0.191215 | −0.0956074 | − | 0.995419i | \(-0.530479\pi\) | ||||
−0.0956074 | + | 0.995419i | \(0.530479\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 26.8328i | − | 1.14520i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17.8885 | + | 12.0000i | −0.762078 | + | 0.511217i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 67.0820i | 2.85262i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18.0000 | −0.762684 | −0.381342 | − | 0.924434i | \(-0.624538\pi\) | ||||
−0.381342 | + | 0.924434i | \(0.624538\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.00000i | 0.0422955i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.4164i | 0.566441i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.0000i | 0.463595i | 0.972764 | + | 0.231797i | \(0.0744606\pi\) | ||||
−0.972764 | + | 0.231797i | \(0.925539\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.8885i | 0.752577i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.47214 | 0.187812 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 44.7214i | − | 1.87482i | −0.348232 | − | 0.937408i | \(-0.613218\pi\) | ||
0.348232 | − | 0.937408i | \(-0.386782\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.8328 | 1.12292 | 0.561459 | − | 0.827504i | \(-0.310240\pi\) | ||||
0.561459 | + | 0.827504i | \(0.310240\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.00000 | −0.334205 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −17.8885 | −0.746004 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.3607i | 0.930887i | 0.885078 | + | 0.465444i | \(0.154105\pi\) | ||||
−0.885078 | + | 0.465444i | \(0.845895\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.47214 | −0.185856 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 20.0000 | 0.829740 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 27.0000i | − | 1.11823i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.00000 | −0.0826898 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −40.2492 | −1.66126 | −0.830632 | − | 0.556822i | \(-0.812020\pi\) | ||||
−0.830632 | + | 0.556822i | \(0.812020\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.0000 | −0.824086 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 22.0000i | 0.904959i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.0000 | −0.451716 | −0.225858 | − | 0.974160i | \(-0.572519\pi\) | ||||
−0.225858 | + | 0.974160i | \(0.572519\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20.0000i | 0.819920i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 4.47214i | − | 0.183032i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.0000i | 0.612883i | 0.951889 | + | 0.306442i | \(0.0991384\pi\) | ||||
−0.951889 | + | 0.306442i | \(0.900862\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 4.47214i | − | 0.182422i | −0.995832 | − | 0.0912111i | \(-0.970926\pi\) | ||
0.995832 | − | 0.0912111i | \(-0.0290738\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −17.8885 | −0.728478 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.00000 | −0.0813116 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.0000i | 0.527654i | 0.964570 | + | 0.263827i | \(0.0849848\pi\) | ||||
−0.964570 | + | 0.263827i | \(0.915015\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 20.0000 | − | 13.4164i | 0.810441 | − | 0.543660i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.00000i | 0.121367i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29.0000 | −1.17130 | −0.585649 | − | 0.810564i | \(-0.699160\pi\) | ||||
−0.585649 | + | 0.810564i | \(0.699160\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.47214 | 0.180334 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 25.0000i | − | 1.00483i | −0.864625 | − | 0.502417i | \(-0.832444\pi\) | ||
0.864625 | − | 0.502417i | \(-0.167556\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 22.3607i | − | 0.897303i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 60.0000i | − | 2.40385i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 12.0000i | − | 0.479234i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.8885 | −0.712132 | −0.356066 | − | 0.934461i | \(-0.615882\pi\) | ||||
−0.356066 | + | 0.934461i | \(0.615882\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 27.0000 | 1.07315 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.0000i | 0.476205i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.0000 | 0.515079 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −17.8885 | −0.707660 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 22.3607i | − | 0.883194i | −0.897214 | − | 0.441597i | \(-0.854412\pi\) | ||
0.897214 | − | 0.441597i | \(-0.145588\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −40.2492 | −1.58727 | −0.793637 | − | 0.608391i | \(-0.791815\pi\) | ||||
−0.793637 | + | 0.608391i | \(0.791815\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.00000 | −0.0393750 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.4164 | 0.527453 | 0.263727 | − | 0.964597i | \(-0.415048\pi\) | ||||
0.263727 | + | 0.964597i | \(0.415048\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.4164i | 0.526640i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 22.3607 | 0.876384 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 4.47214i | − | 0.175008i | −0.996164 | − | 0.0875041i | \(-0.972111\pi\) | ||
0.996164 | − | 0.0875041i | \(-0.0278891\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 17.8885i | 0.697899i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 9.00000i | − | 0.350590i | −0.984516 | − | 0.175295i | \(-0.943912\pi\) | ||
0.984516 | − | 0.175295i | \(-0.0560880\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 42.0000 | 1.63361 | 0.816805 | − | 0.576913i | \(-0.195743\pi\) | ||||
0.816805 | + | 0.576913i | \(0.195743\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.47214 | −0.173683 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 17.8885i | − | 0.693688i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.4164 | + | 20.0000i | 0.519485 | + | 0.774403i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 17.8885i | − | 0.691611i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −40.2492 | −1.55380 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.0000 | 0.732396 | 0.366198 | − | 0.930537i | \(-0.380659\pi\) | ||||
0.366198 | + | 0.930537i | \(0.380659\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 20.0000i | 0.769800i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 35.7771i | − | 1.37503i | −0.726172 | − | 0.687513i | \(-0.758703\pi\) | ||
0.726172 | − | 0.687513i | \(-0.241297\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 60.0000i | − | 2.30259i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 17.8885i | − | 0.685490i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.8885 | 0.684486 | 0.342243 | − | 0.939611i | \(-0.388813\pi\) | ||||
0.342243 | + | 0.939611i | \(0.388813\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 17.8885i | − | 0.683486i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 22.3607 | 0.853113 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.00000 | 0.342873 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.8328 | 1.02077 | 0.510384 | − | 0.859946i | \(-0.329503\pi\) | ||||
0.510384 | + | 0.859946i | \(0.329503\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 26.8328i | − | 1.01929i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.47214 | −0.169638 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.0000 | −0.757554 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.00000i | 0.340411i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.00000 | −0.113308 | −0.0566542 | − | 0.998394i | \(-0.518043\pi\) | ||||
−0.0566542 | + | 0.998394i | \(0.518043\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.00000 | −0.112987 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 40.0000i | − | 1.50435i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.0000 | −1.31445 | −0.657226 | − | 0.753693i | \(-0.728270\pi\) | ||||
−0.657226 | + | 0.753693i | \(0.728270\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 30.0000i | 1.12509i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 22.3607i | 0.837414i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.00000i | 0.112194i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 22.3607i | 0.835075i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.8885 | −0.667130 | −0.333565 | − | 0.942727i | \(-0.608252\pi\) | ||||
−0.333565 | + | 0.942727i | \(0.608252\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17.0000i | 0.632237i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12.0000 | − | 17.8885i | −0.445669 | − | 0.664364i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.0000i | 1.18681i | 0.804902 | + | 0.593407i | \(0.202218\pi\) | ||||
−0.804902 | + | 0.593407i | \(0.797782\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.47214 | 0.165408 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 35.7771i | − | 1.32146i | −0.750625 | − | 0.660728i | \(-0.770247\pi\) | ||
0.750625 | − | 0.660728i | \(-0.229753\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 13.0000i | 0.479512i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 26.8328i | 0.988399i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1.00000i | − | 0.0367856i | −0.999831 | − | 0.0183928i | \(-0.994145\pi\) | ||
0.999831 | − | 0.0183928i | \(-0.00585494\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.00000 | 0.146944 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.0000i | 0.586983i | 0.955962 | + | 0.293492i | \(0.0948173\pi\) | ||||
−0.955962 | + | 0.293492i | \(0.905183\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.00000 | −0.0366372 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.94427 | 0.327254 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 60.0000 | 2.19235 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 40.0000i | − | 1.45962i | −0.683650 | − | 0.729810i | \(-0.739608\pi\) | ||
0.683650 | − | 0.729810i | \(-0.260392\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 23.0000 | 0.838167 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13.4164 | 0.488273 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.3050i | 1.13780i | 0.822407 | + | 0.568899i | \(0.192630\pi\) | ||||
−0.822407 | + | 0.568899i | \(0.807370\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −13.4164 | −0.486985 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.0000 | −1.08750 | −0.543750 | − | 0.839248i | \(-0.682996\pi\) | ||||
−0.543750 | + | 0.839248i | \(0.682996\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.47214 | −0.161902 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.94427i | 0.323381i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.47214 | −0.161479 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 49.1935i | − | 1.77396i | −0.461805 | − | 0.886981i | \(-0.652798\pi\) | ||
0.461805 | − | 0.886981i | \(-0.347202\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 17.0000i | − | 0.612240i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.47214i | 0.160852i | 0.996761 | + | 0.0804258i | \(0.0256280\pi\) | ||||
−0.996761 | + | 0.0804258i | \(0.974372\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 20.0000i | − | 0.718421i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17.8885 | 0.640924 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 26.8328i | 0.960154i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 22.3607 | − | 15.0000i | 0.799106 | − | 0.536056i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 4.47214i | − | 0.159617i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.8328 | 0.956487 | 0.478243 | − | 0.878227i | \(-0.341274\pi\) | ||||
0.478243 | + | 0.878227i | \(0.341274\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21.0000 | 0.747620 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 80.0000i | − | 2.84447i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 13.4164i | − | 0.476431i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9.00000i | 0.319197i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.3607i | 0.792056i | 0.918238 | + | 0.396028i | \(0.129612\pi\) | ||||
−0.918238 | + | 0.396028i | \(0.870388\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.4164 | 0.474638 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 26.8328i | − | 0.948091i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 26.8328 | 0.946910 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −20.0000 | −0.704907 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.47214 | 0.157427 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.8328i | 0.943392i | 0.881761 | + | 0.471696i | \(0.156358\pi\) | ||||
−0.881761 | + | 0.471696i | \(0.843642\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.47214 | 0.157038 | 0.0785190 | − | 0.996913i | \(-0.474981\pi\) | ||||
0.0785190 | + | 0.996913i | \(0.474981\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17.0000 | 0.596216 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.00000i | 0.0350285i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.00000 | −0.139942 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.94427 | 0.312538 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.0000 | 0.872506 | 0.436253 | − | 0.899824i | \(-0.356305\pi\) | ||||
0.436253 | + | 0.899824i | \(0.356305\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 44.0000i | 1.53374i | 0.641800 | + | 0.766872i | \(0.278188\pi\) | ||||
−0.641800 | + | 0.766872i | \(0.721812\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12.0000 | 0.417786 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.0000i | 0.799788i | 0.916561 | + | 0.399894i | \(0.130953\pi\) | ||||
−0.916561 | + | 0.399894i | \(0.869047\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 40.2492i | − | 1.39791i | −0.715164 | − | 0.698957i | \(-0.753648\pi\) | ||
0.715164 | − | 0.698957i | \(-0.246352\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 22.0000i | − | 0.763172i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 58.1378i | − | 2.01435i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.94427 | 0.309529 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 25.0000 | 0.864126 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 5.00000i | − | 0.172619i | −0.996268 | − | 0.0863096i | \(-0.972493\pi\) | ||
0.996268 | − | 0.0863096i | \(-0.0275074\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.0000 | + | 26.8328i | −0.379310 | + | 0.925270i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.00000i | 0.172209i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.0000 | 0.412813 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.94427 | 0.307329 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 4.47214i | − | 0.153483i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.94427i | 0.306246i | 0.988207 | + | 0.153123i | \(0.0489331\pi\) | ||||
−0.988207 | + | 0.153123i | \(0.951067\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 8.00000i | − | 0.273594i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 53.0000 | 1.81045 | 0.905223 | − | 0.424937i | \(-0.139704\pi\) | ||||
0.905223 | + | 0.424937i | \(0.139704\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 15.0000i | − | 0.511793i | −0.966704 | − | 0.255897i | \(-0.917629\pi\) | ||
0.966704 | − | 0.255897i | \(-0.0823707\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −20.0000 | −0.681598 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.94427 | 0.304467 | 0.152233 | − | 0.988345i | \(-0.451353\pi\) | ||||
0.152233 | + | 0.988345i | \(0.451353\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.00000 | −0.204006 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.00000i | 0.101885i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 45.0000 | 1.52652 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.94427 | −0.303065 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 26.8328i | − | 0.908153i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 40.2492 | 1.36067 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −43.0000 | −1.45201 | −0.726003 | − | 0.687691i | \(-0.758624\pi\) | ||||
−0.726003 | + | 0.687691i | \(0.758624\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.94427i | 0.301340i | 0.988584 | + | 0.150670i | \(0.0481431\pi\) | ||||
−0.988584 | + | 0.150670i | \(0.951857\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40.2492 | 1.35449 | 0.677247 | − | 0.735756i | \(-0.263173\pi\) | ||||
0.677247 | + | 0.735756i | \(0.263173\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 4.47214i | − | 0.150329i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 53.0000i | 1.77957i | 0.456384 | + | 0.889783i | \(0.349144\pi\) | ||||
−0.456384 | + | 0.889783i | \(0.650856\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 53.6656i | − | 1.79989i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 3.00000i | − | 0.100504i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.0000 | −0.401565 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −17.8885 | −0.597948 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 4.47214i | − | 0.149320i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −22.3607 | + | 15.0000i | −0.745770 | + | 0.500278i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 40.2492i | − | 1.34090i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.47214 | 0.148823 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 25.0000 | 0.831028 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.0000i | 0.929725i | 0.885383 | + | 0.464862i | \(0.153896\pi\) | ||||
−0.885383 | + | 0.464862i | \(0.846104\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 17.8885i | − | 0.593326i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 55.0000i | − | 1.82223i | −0.412151 | − | 0.911116i | \(-0.635222\pi\) | ||
0.412151 | − | 0.911116i | \(-0.364778\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 13.4164i | − | 0.444018i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 13.4164 | 0.443533 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −53.6656 | −1.77027 | −0.885133 | − | 0.465338i | \(-0.845933\pi\) | ||||
−0.885133 | + | 0.465338i | \(0.845933\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −27.0000 | −0.889680 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.94427 | −0.294404 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 46.0000 | 1.50921 | 0.754606 | − | 0.656179i | \(-0.227828\pi\) | ||||
0.754606 | + | 0.656179i | \(0.227828\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 52.0000i | 1.70423i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13.4164 | 0.438763 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.00000 | 0.0653372 | 0.0326686 | − | 0.999466i | \(-0.489599\pi\) | ||||
0.0326686 | + | 0.999466i | \(0.489599\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 1.00000i | − | 0.0326338i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −33.0000 | −1.07577 | −0.537885 | − | 0.843018i | \(-0.680776\pi\) | ||||
−0.537885 | + | 0.843018i | \(0.680776\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 20.0000i | − | 0.651290i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 22.3607i | 0.727393i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 27.0000i | − | 0.877382i | −0.898638 | − | 0.438691i | \(-0.855442\pi\) | ||
0.898638 | − | 0.438691i | \(-0.144558\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.94427i | 0.290343i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.47214 | 0.145019 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 39.0000 | 1.26333 | 0.631667 | − | 0.775240i | \(-0.282371\pi\) | ||||
0.631667 | + | 0.775240i | \(0.282371\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.00000i | 0.258874i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.00000 | − | 13.4164i | −0.290929 | − | 0.433691i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 80.0000i | 2.58333i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.00000 | 0.193548 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 26.8328 | 0.864675 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.47214i | 0.143963i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.00000i | 0.225105i | 0.993646 | + | 0.112552i | \(0.0359026\pi\) | ||||
−0.993646 | + | 0.112552i | \(0.964097\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 17.8885i | − | 0.574663i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.0000i | 0.641831i | 0.947108 | + | 0.320915i | \(0.103990\pi\) | ||||
−0.947108 | + | 0.320915i | \(0.896010\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.0000 | 0.641171 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.00000i | 0.128103i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −43.0000 | −1.37569 | −0.687846 | − | 0.725857i | \(-0.741444\pi\) | ||||
−0.687846 | + | 0.725857i | \(0.741444\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −40.2492 | −1.28637 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.00000 | −0.0638551 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 9.00000i | − | 0.287055i | −0.989646 | − | 0.143528i | \(-0.954155\pi\) | ||
0.989646 | − | 0.143528i | \(-0.0458446\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22.0000 | 0.700978 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 13.4164 | 0.427049 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.47214i | 0.142206i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 15.0000 | 0.476011 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.47214 | −0.141776 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.8885i | 0.566536i | 0.959041 | + | 0.283268i | \(0.0914186\pi\) | ||||
−0.959041 | + | 0.283268i | \(0.908581\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1856.2.e.h.1217.2 | 4 | ||
4.3 | odd | 2 | inner | 1856.2.e.h.1217.3 | 4 | ||
8.3 | odd | 2 | 928.2.e.b.289.1 | ✓ | 4 | ||
8.5 | even | 2 | 928.2.e.b.289.4 | yes | 4 | ||
29.28 | even | 2 | inner | 1856.2.e.h.1217.4 | 4 | ||
116.115 | odd | 2 | inner | 1856.2.e.h.1217.1 | 4 | ||
232.115 | odd | 2 | 928.2.e.b.289.3 | yes | 4 | ||
232.173 | even | 2 | 928.2.e.b.289.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
928.2.e.b.289.1 | ✓ | 4 | 8.3 | odd | 2 | ||
928.2.e.b.289.2 | yes | 4 | 232.173 | even | 2 | ||
928.2.e.b.289.3 | yes | 4 | 232.115 | odd | 2 | ||
928.2.e.b.289.4 | yes | 4 | 8.5 | even | 2 | ||
1856.2.e.h.1217.1 | 4 | 116.115 | odd | 2 | inner | ||
1856.2.e.h.1217.2 | 4 | 1.1 | even | 1 | trivial | ||
1856.2.e.h.1217.3 | 4 | 4.3 | odd | 2 | inner | ||
1856.2.e.h.1217.4 | 4 | 29.28 | even | 2 | inner |